# An Empirical Comparison of Cost Functions in Inductive Logic Programming

arXiv: https://arxiv.org/abs/2503.07554 · HTML: https://mlsanity.com/paper/2503.07554/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 90 references that are in the map.
- First posted on arXiv 10 Mar 2025.

## Builds on (most cited first, 22 of 22)

- [Visual Genome: Connecting Language and Vision Using Crowdsourced Dense Image Annotations](https://mlsanity.com/paper/1602.07332/) (2016)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [Hypothesis Search: Inductive Reasoning with Language Models](https://mlsanity.com/paper/2309.05660/) (2023)
- [The ConceptARC Benchmark: Evaluating Understanding and Generalization in the ARC Domain](https://mlsanity.com/paper/2305.07141/) (2023)
- [Inductive logic programming at 30: a new introduction](https://mlsanity.com/paper/2008.07912/) (2020)
- [LLMs and the Abstraction and Reasoning Corpus: Successes, Failures, and the Importance of Object-based Representations](https://mlsanity.com/paper/2305.18354/) (2023)
- [Learning programs by learning from failures](https://mlsanity.com/paper/2005.02259/) (2020)
- [A Semantic Matching Energy Function for Learning with Multi-relational Data](https://mlsanity.com/paper/1301.3485/) (2013)
- [Few-Shot Bayesian Imitation Learning with Logical Program Policies](https://mlsanity.com/paper/1904.06317/) (2019)
- [BUSTLE: Bottom-Up Program Synthesis Through Learning-Guided Exploration](https://mlsanity.com/paper/2007.14381/) (2020)
- [Making sense of sensory input](https://mlsanity.com/paper/1910.02227/) (2019)
- [Neuro-Symbolic Hierarchical Rule Induction](https://mlsanity.com/paper/2112.13418/) (2021)
- [Inductive Learning of Answer Set Programs from Noisy Examples](https://mlsanity.com/paper/1808.08441/) (2018)
- [Randomised Gaussian Process Upper Confidence Bound for Bayesian Optimisation](https://mlsanity.com/paper/2006.04296/) (2020)
- [Inductive general game playing](https://mlsanity.com/paper/1906.09627/) (2019)
- [Just-in-Time Learning for Bottom-Up Enumerative Synthesis](https://mlsanity.com/paper/2010.08663/) (2020)
- [Learning MDL logic programs from noisy data](https://mlsanity.com/paper/2308.09393/) (2023)
- [Optimal or Greedy Decision Trees? Revisiting their Objectives, Tuning, and Performance](https://mlsanity.com/paper/2409.12788/) (2024)
- [Inductive Program Synthesis Over Noisy Data](https://mlsanity.com/paper/2009.10272/) (2020)
- [Learning logic programs by combining programs](https://mlsanity.com/paper/2206.01614/) (2022)
- [Program Synthesis with Best-First Bottom-Up Search](https://mlsanity.com/paper/2310.04327/) (2023)
- [Relational decomposition for program synthesis](https://mlsanity.com/paper/2408.12212/) (2024)

## Abstract (arXiv)

Recent inductive logic programming (ILP) approaches learn optimal hypotheses. An optimal hypothesis minimises a given cost function on the training data. There are many cost functions, such as minimising training error, textual complexity, or the description length of hypotheses. However, selecting an appropriate cost function remains a key question. To address this gap, we extend a constraint-based ILP system to learn optimal hypotheses for seven standard cost functions. We then empirically compare the generalisation error of optimal hypotheses induced under these standard cost functions. Our results on over 20 domains and 1000 tasks, including game playing, program synthesis, and image reasoning, show that, while no cost function consistently outperforms the others, minimising training error or description length has the best overall performance. Notably, our results indicate that minimising the size of hypotheses does not always reduce generalisation error.